We present magnetostriction and magnetization measurements of a cobalt ferrite Co0.8Fe2.2O4 single crystal. We observe unusual behaviour in the magnetic hard axis of the single crystal which manifests in a jump of the magnetization curve at a critical field. This first order magnetization process (FOMP) which is explained as an anisotropy driven transition is visible at temperatures lower than 150 K. By analyzing the anisotropy constants we found that the higher order anisotropy constant K2 dominates the anisotropy energy. In the magnetostriction measurements the FOMP is clearly visible as a huge jump in the [111] direction, which can be explained by means of a geometric model. ; Comment: This Paper is already accepted for the conference proceedings of the MMM 2011 (http://www.magnetism.org). The proceedings will be published in April 2012 in Journal of Applied Physics